Partial Frequencies and Chladni’s Law in Church Bells

Partial Frequencies and Chladni’s Law in Church Bells

The rim partials of a church bell (those with an antinode at the soundbow) generate the strike pitch or perceived note of the bell. The spacing in frequency of the higher rim partials has an important effect on the tonal quality of the bell. Investigations into the partial frequencies of 2752 bells, both bronze and steel, of a wide variety of dates, founders and sizes, show a simple and unexpec...

Virtual Pitch and Pitch Shifts in Church Bells

It is well established that musical sounds comprising multiple partials with frequencies approximately in the ratio of small integers give rise to a strong sensation of pitch even if the lowest or fundamental partial is missing—the so-called virtual pitch effect. Experiments on thirty test subjects demonstrate that this virtual pitch is shifted significantly by changes in the spacing of the con...

Dispensations provide for flexibility in church law.

Exact Radial Free Vibration Frequencies of Power-Law Graded Spheres

This study concentrates on the free pure radial vibrations of hollow spheres made of hypothetically functionally simple power rule graded materials having identical inhomogeneity indexes for both Young’s modulus and the density in an analytical manner. After offering the exact elements of the free vibration coefficient matrices for free-free, free-fixed, and fixed-fixed restraints, a parametric...

The Need for a Law of Church and Market

The study of law and religion has tended to focus on debates over “church and state.” The central question has been how the law ought to structure the relationship between religion and the government. Many of the legal conflicts over religion, however, take place in a commercial context. They are thus not simply puzzles of how God and Caesar should interact. They also present the question of ho...